1-2
PropertiesofofReal
RealNumbers
Numbers
1-2 Properties
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Opener-SAME SHEET-3/17
Simplify.
1. –5+5
0
2.
1
3.
1.81
4. Find 10% of $61.70. $6.17
5. Find the reciprocal of –4.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Objective
Identify and use properties of real
numbers.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
The four basic math operations are
addition, subtraction, multiplication,
and division. Because subtraction is
addition of the opposite and division
is multiplication by the reciprocal, the
properties of real numbers focus on
addition and multiplication.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Properties Real Numbers
Identities and Inverses
For all real numbers n,
WORDS
Additive Identity Property
The sum of a number and 0, the additive
identity, is the original number.
NUMBERS
3+0=0
ALGEBRA
n+0=0+n=n
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Properties Real Numbers
Identities and Inverses
For all real numbers n,
WORDS
Multiplicative Identity Property
The product of a number and 1, the
multiplicative identity, is the original
number.
NUMBERS
ALGEBRA
Holt McDougal Algebra 2
n1=1n=n
1-2 Properties of Real Numbers
Properties Real Numbers
Identities and Inverses
For all real numbers n,
WORDS
Additive Inverse Property
The sum of a number and its opposite,
or additive inverse, is 0.
NUMBERS
5 + (–5) = 0
ALGEBRA
n + (–n) = 0
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Properties Real Numbers
Identities and Inverses
For all real numbers n,
WORDS
Multiplicative Inverse Property
The product of a nonzero number and its
reciprocal, or multiplicative inverse, is 1.
NUMBERS
ALGEBRA
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Recall from previous courses that the opposite of
any number a is –a and the reciprocal of any
nonzero number a is .
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Example 1A: Finding Inverses
Find the additive and multiplicative inverse of
each number.
12
Holt McDougal Algebra 2
500
1-2 Properties of Real Numbers
Reading Math
Based on the Closure Property, the real numbers
are said to be closed under addition and closed
under multiplication.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Example 2: Identifying Properties of Real Numbers
Identify the property demonstrated by each
question.
A. 2  3.9 = 3.9  2
B.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Signs
• Partners will make signs for each of the
properties
Add ident
Closure
Mult Ident
Commutative
Add inverse
Associative
Mult inverse
Distributive
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Example 3: Consumer Economics Application
Use mental math to find a 5% tax on a $42.40
purchase.
A 5% tax on a $42.40 is $2.12.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Check It Out! Example 3
Use mental math to find a 20% discount on
a $15.60 shirt.
A 20% discount on a $15.60 shirt is $3.12.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Opener-SAME SHEET-3/18
Find the additive and multiplicative inverse of
each number.
1. –15 15;
2.
;
Identify the property demonstrated by
each question.
3.
4.
Commutative Property of Addition
Distributive Property
5. Use mental math to find a 15% tip for a
$ 64.20 bill. $9.63
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
1-2 Wkst
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Quiz
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Example 4A: Classifying Statements as Sometimes,
Always, or Never True
Classifying each statement as sometimes,
always, or never true. Give examples or
properties to support your answers.
a  b = a, where b = 3
sometimes true
true example: 0  3 = 0
false example: 1  3 ≠ 1
Holt McDougal Algebra 2
True and false
examples exist. The
statement is true
when a = 0 and false
when a ≠ 0.
1-2 Properties of Real Numbers
Example 4B: Classifying Statements as Sometimes,
Always, or Never True
Classifying each statement as sometimes,
always, or never true. Give examples or
properties to support your answers.
3(a + 1) = 3a + 3
always true
Holt McDougal Algebra 2
Always true by the
Distributive Property.
1-2 Properties of Real Numbers
Check It Out! Example 4a
Classify each statement as sometimes, always,
or never true. Give examples or properties to
support your answer.
a + (–a) = b + (–b)
Always true by the Additive Inverse Property.
Holt McDougal Algebra 2
1-2 Properties of Real Numbers
Check It Out! Example 4b
Classify each statement as sometimes, always,
or never true. Give examples or properties to
support your answer.
a – (b + c) = (a – b) + (a – c)
sometimes true
true example:
0 – (1 + 2) = (0 – 1) + (0 – 2)
–3 = –3
false example:
1 – (2 + 3) = (1 – 2) + (1 – 3)
–4 ≠ –3
Holt McDougal Algebra 2
True and false
examples exist. The
statement is true
when a = 0, b = 1,
and c = 2. False
when a = 1, b = 2,
and c = 3.